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‎07_Simple_and_Multiple_Regression.ipynb

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"base_uri": "https://localhost:8080/",
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"height": 73
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},
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"outputId": "a3ee0a12-0104-4c4c-b4ae-58c4d1790fde"
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"outputId": "b942fff1-46a4-493e-fee0-55b910ae3173"
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},
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"source": [
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"# Libraries \n",
@@ -67,7 +67,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 204
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},
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"outputId": "28170068-8b0a-41d0-c232-52ad620b6004"
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"outputId": "35052345-2dba-4323-a36a-1f0c33c64279"
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},
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"source": [
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"# Load the Datasets (For indepth analysis please refer to Part O1 All About Datasets)\n",
@@ -236,7 +236,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 395
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},
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"outputId": "c0ba3c2a-5d1b-4fcd-b45b-345f8ab0f690"
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"outputId": "e3a6efdc-4e96-41de-86ad-50ccabb17b41"
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},
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"source": [
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"# Dataset overall Information\n",
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"base_uri": "https://localhost:8080/",
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"height": 107
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},
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"outputId": "5d67a37d-833e-4520-e101-ad5403a54b30"
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"outputId": "349a9591-0a95-4e8a-a892-bad733ee880e"
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},
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"source": [
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"# Let set the BASE MODEL on which we will improve\n",
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"base_uri": "https://localhost:8080/",
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"height": 688
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},
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"outputId": "625eb866-7bfd-4aec-e722-d6b968cc4d0a"
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"outputId": "864677de-26f1-4b44-cbf5-d665de057d4f"
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},
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"source": [
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"# Base Model\n",
@@ -349,7 +349,7 @@
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" <th>Date:</th> <td>Wed, 02 Sep 2020</td> <th> Prob (F-statistic):</th> <td>2.38e-320</td>\n",
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"</tr>\n",
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"<tr>\n",
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" <th>Time:</th> <td>11:15:35</td> <th> Log-Likelihood: </th> <td> -1556.1</td> \n",
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" <th>Time:</th> <td>11:18:47</td> <th> Log-Likelihood: </th> <td> -1556.1</td> \n",
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"</tr>\n",
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"<tr>\n",
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" <th>No. Observations:</th> <td> 506</td> <th> AIC: </th> <td> 3136.</td> \n",
@@ -429,7 +429,7 @@
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"Model: OLS Adj. R-squared (uncentered): 0.953\n",
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"Method: Least Squares F-statistic: 846.6\n",
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"Date: Wed, 02 Sep 2020 Prob (F-statistic): 2.38e-320\n",
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"Time: 11:15:35 Log-Likelihood: -1556.1\n",
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"Time: 11:18:47 Log-Likelihood: -1556.1\n",
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"No. Observations: 506 AIC: 3136.\n",
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"Df Residuals: 494 BIC: 3187.\n",
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"Df Model: 12 \n",
@@ -479,7 +479,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 755
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},
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"outputId": "a909a773-e369-40bf-edad-6c72f05aa72b"
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"outputId": "60b78f0e-9956-4d18-b995-b5a0882a5d58"
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},
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"source": [
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"# Model Properties\n",
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"base_uri": "https://localhost:8080/",
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"height": 89
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},
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"outputId": "1c03ab7c-c0fe-48f9-ab84-b87a2dd2dc55"
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"outputId": "76569343-32db-4b52-9b67-33305321afc4"
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},
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"source": [
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"# Let test the Base Model\n",
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"base_uri": "https://localhost:8080/",
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"height": 688
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},
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"outputId": "29556eda-af03-43fc-e4c9-577b78a47df1"
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"outputId": "d1d85ad3-f047-48d1-ebab-f923ec7febaa"
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},
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"source": [
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"# Base Model\n",
@@ -731,7 +731,7 @@
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" <th>Date:</th> <td>Wed, 02 Sep 2020</td> <th> Prob (F-statistic):</th> <td>1.06e-223</td>\n",
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"</tr>\n",
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"<tr>\n",
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" <th>Time:</th> <td>11:15:35</td> <th> Log-Likelihood: </th> <td> -1078.0</td> \n",
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" <th>Time:</th> <td>11:18:48</td> <th> Log-Likelihood: </th> <td> -1078.0</td> \n",
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"</tr>\n",
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"<tr>\n",
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" <th>No. Observations:</th> <td> 354</td> <th> AIC: </th> <td> 2180.</td> \n",
@@ -811,7 +811,7 @@
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"Model: OLS Adj. R-squared (uncentered): 0.954\n",
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"Method: Least Squares F-statistic: 619.5\n",
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"Date: Wed, 02 Sep 2020 Prob (F-statistic): 1.06e-223\n",
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"Time: 11:15:35 Log-Likelihood: -1078.0\n",
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"Time: 11:18:48 Log-Likelihood: -1078.0\n",
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"No. Observations: 354 AIC: 2180.\n",
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"Df Residuals: 342 BIC: 2226.\n",
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"Df Model: 12 \n",
@@ -861,7 +861,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 89
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},
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"outputId": "14e5ec3d-d30a-4dde-f243-697d9b857e6b"
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"outputId": "7e5f7f5c-c2b6-4044-e3df-bfb5c09fe978"
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},
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"source": [
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"# Base Model Test and Metrics\n",
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"base_uri": "https://localhost:8080/",
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"height": 668
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},
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"outputId": "5948c239-5cc0-4c5a-d270-ae4b03535302"
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"outputId": "72050626-3b7d-484b-b626-c24febbd8ff6"
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},
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"source": [
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"# Model 2, let do some data cleaning\n",
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fc1a2aacef0>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fa4ec497eb8>"
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]
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},
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"metadata": {
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"base_uri": "https://localhost:8080/",
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"height": 421
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},
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"outputId": "a5d701eb-ab8c-4b3f-e649-ce78d8d5099e"
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"outputId": "393561f7-f1eb-4b04-ac15-27e05e88db26"
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},
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"source": [
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"# Filtering Highly Positive or Negative Correlated Values\n",
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"base_uri": "https://localhost:8080/",
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"height": 89
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},
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"outputId": "80b3e50b-abb0-4d11-c254-b1a7bb73e7ad"
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"outputId": "58adb35d-61b0-4d33-d4f6-fffdfe530224"
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},
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"source": [
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"# Find index of feature columns with correlation greater than 0.75\n",
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"base_uri": "https://localhost:8080/",
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"height": 517
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},
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"outputId": "a9a4751a-d915-4276-f53d-7fd6c6ff014e"
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"outputId": "3be53026-e6b3-4f46-a6d6-ee74b7a8546e"
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},
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"source": [
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"# Now check Outlier in the data\n",
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"base_uri": "https://localhost:8080/",
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"height": 535
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},
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"outputId": "efc04a52-9e44-4af5-ddfe-1161bfeedfe1"
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"outputId": "cf78a8dc-8237-40c4-b64f-e817e009a684"
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},
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"source": [
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"# ZN Column\n",
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fc1a2aac780>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fa4e7320080>"
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]
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},
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"metadata": {
@@ -1435,7 +1435,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 535
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},
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"outputId": "c9505075-8b9a-40d6-b26b-088afe6a838b"
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"outputId": "49ff2c16-77f8-462b-9beb-6dd165edcb63"
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},
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"source": [
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"# CRIM Column\n",
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fc19f604fd0>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fa4e72acba8>"
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]
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},
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"metadata": {
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"base_uri": "https://localhost:8080/",
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"height": 517
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},
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"outputId": "912f850a-3176-47fb-e4fe-a889b62be5c3"
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"outputId": "29fcab85-2354-4406-8497-89ee77dc4fe1"
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},
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"source": [
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"# CHAS Column\n",
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"base_uri": "https://localhost:8080/",
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"height": 535
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},
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"outputId": "a2c2de83-cf0c-4871-c589-f2c180d05ac2"
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"outputId": "46ae1502-1750-4dfd-d2f0-faca0788c0b5"
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},
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"source": [
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"# AGE Column \n",
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fc19d80a860>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fa4e71f9fd0>"
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]
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},
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"metadata": {
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"base_uri": "https://localhost:8080/",
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"height": 517
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},
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"outputId": "f2f76a7c-e752-4c57-e572-a5173ec04a56"
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"outputId": "408fe42d-abb0-4361-b60e-10fd52f0b156"
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},
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"source": [
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"# DIS Column\n",
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"base_uri": "https://localhost:8080/",
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"height": 535
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},
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"outputId": "34d2f9a5-fff0-4d19-914f-66d4e8994e2e"
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"outputId": "051626d0-b0bc-40cd-d446-6bc8e53d4da5"
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},
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"source": [
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"# RAD Column \n",
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fc19d76a4a8>"
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"<matplotlib.axes._subplots.AxesSubplot at 0x7fa4e71599e8>"
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]
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},
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"metadata": {
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"base_uri": "https://localhost:8080/",
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"height": 517
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},
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"outputId": "86733563-e5c5-4ec4-88ef-844ba5cec7a6"
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"outputId": "24bc009c-15cd-4fbd-9b6d-3ba75ce51561"
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},
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"source": [
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"# B Column\n",
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"base_uri": "https://localhost:8080/",
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"height": 266
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},
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"outputId": "5c5e6409-3cc3-4108-d3f1-0561b3f19b48"
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"outputId": "21451197-0d54-4fe3-aab1-7b42ef5e6cd3"
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},
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"source": [
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"# Lets check Skewness in the Data\n",
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"base_uri": "https://localhost:8080/",
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"height": 143
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},
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"outputId": "b271b85d-1eac-4be1-93f3-c6b71cb21f24"
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"outputId": "45014745-cddc-4761-b371-47b455fe4a58"
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},
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"source": [
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"# Lets remove Skewness one by one\n",
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"base_uri": "https://localhost:8080/",
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"height": 181
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},
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"outputId": "d788a1e6-5981-458e-8502-1c5b7c68be15"
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"outputId": "81cf6594-e560-4da9-cbc8-916dbb421812"
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},
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"source": [
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"# ZN Variable\n",
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"base_uri": "https://localhost:8080/",
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"height": 143
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},
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"outputId": "361702f4-29b1-431f-947a-c3ccadcc5053"
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"outputId": "bbc21ebe-22e3-4f62-d8cf-f3f2a18968cd"
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},
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"source": [
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"# B Variable\n",
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"base_uri": "https://localhost:8080/",
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"height": 204
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},
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"outputId": "0e3a12f1-f55e-4c9e-c511-0dd0aac61f36"
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"outputId": "0d27725b-4371-4ab9-ea94-617c90ef6169"
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},
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"source": [
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"# Removing variables (raw variables) which are transformed and keep one set also (no removing)\n",
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"base_uri": "https://localhost:8080/",
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"height": 549
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},
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"outputId": "9c382304-e0b3-4d83-9a65-3dffe61fed16"
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"outputId": "ed95ef32-583d-4138-caa0-32296fba66d7"
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},
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"source": [
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"# Now lets train the model\n",
@@ -2253,7 +2253,7 @@
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" <th>Date:</th> <td>Wed, 02 Sep 2020</td> <th> Prob (F-statistic):</th> <td>8.87e-181</td>\n",
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"</tr>\n",
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"<tr>\n",
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" <th>Time:</th> <td>11:15:38</td> <th> Log-Likelihood: </th> <td> -1196.2</td> \n",
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" <th>Time:</th> <td>11:18:51</td> <th> Log-Likelihood: </th> <td> -1196.2</td> \n",
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"</tr>\n",
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"<tr>\n",
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" <th>No. Observations:</th> <td> 354</td> <th> AIC: </th> <td> 2406.</td> \n",
@@ -2318,7 +2318,7 @@
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"Model: OLS Adj. R-squared (uncentered): 0.912\n",
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"Method: Least Squares F-statistic: 528.2\n",
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"Date: Wed, 02 Sep 2020 Prob (F-statistic): 8.87e-181\n",
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"Time: 11:15:38 Log-Likelihood: -1196.2\n",
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"Time: 11:18:51 Log-Likelihood: -1196.2\n",
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"No. Observations: 354 AIC: 2406.\n",
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"Df Residuals: 347 BIC: 2434.\n",
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"Df Model: 7 \n",
@@ -2361,7 +2361,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 89
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},
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"outputId": "7722cf1c-6236-4b70-867e-46acdff4de25"
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"outputId": "62c653ac-c601-4e2c-8350-b787e4c009d3"
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},
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"source": [
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"# Prediction of Model 2 \n",
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"base_uri": "https://localhost:8080/",
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"height": 507
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},
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"outputId": "4b45c80b-7cc1-4260-8a9f-8b51107ea8f9"
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"outputId": "ab66b478-3e63-406d-bcd5-0b958375ff33"
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},
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"source": [
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"# Model 3\n",
@@ -2443,7 +2443,7 @@
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" <th>Date:</th> <td>Wed, 02 Sep 2020</td> <th> Prob (F-statistic):</th> <td>5.60e-182</td>\n",
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"</tr>\n",
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"<tr>\n",
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" <th>Time:</th> <td>11:15:38</td> <th> Log-Likelihood: </th> <td> -1200.1</td> \n",
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" <th>Time:</th> <td>11:18:51</td> <th> Log-Likelihood: </th> <td> -1200.1</td> \n",
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"</tr>\n",
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"<tr>\n",
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" <th>No. Observations:</th> <td> 354</td> <th> AIC: </th> <td> 2410.</td> \n",
@@ -2502,7 +2502,7 @@
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"Model: OLS Adj. R-squared (uncentered): 0.911\n",
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"Method: Least Squares F-statistic: 726.0\n",
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"Date: Wed, 02 Sep 2020 Prob (F-statistic): 5.60e-182\n",
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"Time: 11:15:38 Log-Likelihood: -1200.1\n",
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"Time: 11:18:51 Log-Likelihood: -1200.1\n",
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"No. Observations: 354 AIC: 2410.\n",
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"Df Residuals: 349 BIC: 2430.\n",
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"Df Model: 5 \n",
@@ -2543,7 +2543,7 @@
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"base_uri": "https://localhost:8080/",
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"height": 89
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},
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"outputId": "d230f68a-87e8-40ac-e5d8-4a2e487d5802"
2546+
"outputId": "92f764cc-3387-4a8f-c22d-dea8f934f75e"
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},
25482548
"source": [
25492549
"# Prediction of Model 3\n",

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